Diffusion in melts

Table 1. Dimensionless values of parameters in the Solutal Model for two cases studied here. The systems I and II are representative of the thermophysical properties of the succinonitrile-acetone systems with differing values of the dif-fusivity ratio Rm, temperature gradient G and capillary parameter F. System III corresponds to parameters for a Pb-Sb alloy with equal diffusivities in melt and crystal...

Iida-Guthrie s empirical expression for self-diffusivity in melt at Dlm (cm2/s) Dlm= 3.5xlO-6fe1/2Fm1/3 M [152]... 

Figure 3-37 Compositional dependence of diffusivities. (a) Fe-Mg interdiffusivity along the c-axis in olivine as a hinction of fayalite content at P — O.l MPa and log /b2 =-6.9 0.1. Diffusion data are extracted using Boltzmann analysis. Some of the nonsmoothness is likely due to uncertainty in extracting interdiffusivity using the Boltzmann method. Data are from Chakraborty (1997). (b) Ar and CO2 diffusivity in melt as a function of H2O content. Data are from Watson (1991b) and Behrens and Zhang (2001).

A value of c equal to 0.3, previously used to describe FT selectivity data on Ru catalysts (4), was also chosen here to describe the behavior of cobalt catalysts. This equation for hydrocarbon diffusion in melts reflects the strong influence of molecular size in reptation and entanglement models of transport in such systems (IJ6). Our model also requires the input of intrinsic values for jSn (given by the asymptotic j8r), jSo, j8r, and j8s, measured independently. After such parameters are specified, the model yields a non-Flory carbon number distribution of increasingly paraffinic hydrocarbons that agrees well with our experimental observations (Fig. 16). 

An important consideration in the existence of a spinodal is the prescribed experimental conditions. In a monodisperse melt, liquid liquid coexistence can only occur along a line in the pressure-temperature/>—T plane. Hence, liquid liquid phase separation under isobaric conditions can only be transient, before the entire phase reverts to the dense liquid. On the other hand, an isochoric quench would be expected to yield true spinodal-like behaviour. The true system is probably something between the two extremes, with volume leaving the system on some timescale. Based on estimates of thermal diffusivity in melts, the time to shrink is of order 10 s (based on a 1 m sample thickness). If... 

If the surface process is very fast (x > and h > x), the volatilization is controlled by diffusion in melt,... 

Water diffusion in melts can be measured during either addition or removal of water. Most studies are based on addition of water by exposure of the melt to flowing air or nitrogen saturated by passing the... 

Schweizer and collaborators have elaborated an extensive mode-coupling model of polymer dynamics [52-54]. The model does not make obvious assumptions about the nature of polymer motion or the presence or absence of particular long-lived dynamic structures, e.g., tubes it yields a set of generalized Langevin equations and associated memory functions. Somewhat realistic assumptions are made for the equilibrium structure of the solutions. Extensive calculations were made of the molecular weight dependences for probe diffusion in melts, often leading by calculation rather than assumption to power-law behaviors for various transport coefficients. However, as presented in the papers noted here, the model is applicable to melts rather than solutions Momentum variables have been completely suppressed, so there are no hydrodynamic interactions. Readers should recall that hydrodynamic interactions usually refer to interactions that are solvent-mediated. 

G. Fleischer, "Self-diffusion in Melts of Polystyrene and Polyethylene Measured by Pulsed Field Gradient NMR," Polvm. Bull. 2., 152-158 (1983). 

G. Fleischer, "The Chain Length Dependence of Self-diffusion in Melts of Polyethylene," Colloid Polvm. Sci.. 265. 89-95 (1987). 

S. F. Tead and E. J. Kramer. Polymer diffusion in melt blends of low and high molecular weight. Macromolecules, 21 (1988), 1513-1517. 

Cell, C. B., Graessley, W. W., Efstratiadis, V., Pitsikalis, M., Hadjichristidis, N. Viscoelasticity and self-diffusion in melts of entangled asymmetric star polymers./. Polym Sci., B, Polym Phys. (1997) 35, pp. 1943-1954... 

In dilute solutions, tire dependence of tire diffusion coefficient on tire molecular weight is different from tliat found in melts, eitlier entangled or not. This difference is due to tire presence of hydrodynamic interactions among tire solvent molecules. Such interactions arise from tire necessity to transfer solvent molecules from tire front to tire back of a moving particle. The motion of tire solvent gives rise to a flow field which couples all molecules over a... 

Termination. The conversion of peroxy and alkyl radicals to nonradical species terminates the propagation reactions, thus decreasing the kinetic chain length. Termination reactions (eqs. 7 and 8) are significant when the oxygen concentration is very low, as in polymers with thick cross-sections where the oxidation rate is controlled by the diffusion of oxygen, or in a closed extmder. The combination of alkyl radicals (eq. 7) leads to cross-linking, which causes an undesirable increase in melt viscosity. 

Hydrated bilayers containing one or more lipid components are commonly employed as models for biological membranes. These model systems exhibit a multiplicity of structural phases that are not observed in biological membranes. In the state that is analogous to fluid biological membranes, the liquid crystal or La bilayer phase present above the main bilayer phase transition temperature, Ta, the lipid hydrocarbon chains are conforma-tionally disordered and fluid ( melted ), and the lipids diffuse in the plane of the bilayer. At temperatures well below Ta, hydrated bilayers exist in the gel, or Lp, state in which the mostly all-trans chains are collectively tilted and pack in a regular two-dimensional... 

In Section 4.2.2 the central role of atomic diffusion in many aspects of materials science was underlined. This is equally true for polymers, but the nature of diffusion is quite different in these materials, because polymer chains get mutually entangled and one chain cannot cross another. An important aspect of viscoelastic behavior of polymer melts is memory such a material can be deformed by hundreds of per cent and still recover its original shape almost completely if the stress is removed after a short time (Ferry 1980). This underlies the use of shrink-fit cling-film in supermarkets. On the other hand, because of diffusion, if the original stress is maintained for a long time, the memory of the original shape fades. 

Fuel matrix - Fission products, bound in a ceramic matrix, may escape only by slow diffusion or melting of the matrix. 

The obvious method of reducing corrosion in fused salts is to choose a system in which either the metal can come to equilibrium with the melt, or else truly protective passivity can be attained. In most cases in industry neither of these alternatives is used. In fact, fused salt baths are usually operated in air atmosphere, and the problem is the prevention of excessive corrosion. This can be done in two ways, (a) by reducing rates of ingress of oxidising species (mainly O2 and H2O) from the atmosphere, and rates of their diffusion in the melts, and (b) by keeping the oxidising power (redox potential) of the melt low by making periodic additions to the bath. 

There are a number of differences between interstitial and substitutional solid solutions, one of the most important of which is the mechanism by which diffusion occurs. In substitutional solid solutions diffusion occurs by the vacancy mechanism already discussed. Since the vacancy concentration and the frequency of vacancy jumps are very low at ambient temperatures, diffusion in substitutional solid solutions is usually negligible at room temperature and only becomes appreciable at temperatures above about 0.5T where is the melting point of the solvent metal (K). In interstitial solid solutions, however, diffusion of the solute atoms occurs by jumps between adjacent interstitial positions. This is a much lower energy process which does not involve vacancies and it therefore occurs at much lower temperatures. Thus hydrogen is mobile in steel at room temperature, while carbon diffuses quite rapidly in steel at temperatures above about 370 K. 

Maklakov AI, Skirde VD, Fatkullin NF (1987) Self-diffusion in polymer solutions and melts (in Russian). University Publ, Kazan... 

Diffusion of ions can be observed in multicomponent systems where concentration gradients can arise. In individnal melts, self-diffnsion of ions can be studied with the aid of radiotracers. Whereas the mobilities of ions are lower in melts, the diffusion coefficients are of the same order of magnitude as in aqueous solutions (i.e., about 10 cmVs). Thus, for melts the Nemst relation (4.6) is not applicable. This can be explained in terms of an appreciable contribntion of ion pairs to diffusional transport since these pairs are nncharged, they do not carry cnrrent, so that values of ionic mobility calculated from diffusion coefficients will be high. 

Radon is a noble gas and is therefore not readily ionized or chemically reactive. Its properties in terrestrial material will be controlled by its solubility in melt and fluid as well as its diffusion coefficients. Compared with the lighter noble gases, Rn diffuses more slowly and has a lower solubility in water. It will also more readily adsorb onto surface that the lighter rare gases. It can, however be lost by degassing in magmatic systems (Condomines et al. 2003). More information about the behavior of Rn can be found in Ivanovich and Harmon (1992). 

Gauthier P-J, Condomines M, Hammouda T (1999) An experimental investigation of radon diffusion in an anhydrous andesitic melt at atmospheric pressure Implications for radon degassing from empting magmas. Geochim Cosmochim Acta 63 645-656... 

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